4(iii)
Construct a regular hexagon of side 4.5 cm. Hence, construct a circle circumscribing the regular hexagon. Use ruler and compass for the construction. Measure and write down the radius of the circle.
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Each interior angle of a regular hexagon = $\Big(\frac{2n - 4}{n}\Big) \times 90°$
= $\Big(\frac{2 \times 6 - 4}{6}\Big) \times 90°$
= 8 × 15°
= 120°.
Steps of Construction:
Draw a regular hexagon ABCDEF with each side equal to 4.5 cm and each interior angle = 120°.
Draw the perpendicular bisectors of AB and AF which intersect each other at O.
With O as center and OA as radius draw a circle which will pass through all the vertices of the regular hexagon.
Measure OF.
From figure,
OF(Radius) = 4.5 cm
Hence, radius of circle = 4.5 cm.